The flow inside cavities between corotating compressor disks of aero-engines is driven by buoyancy, with Grashof numbers exceeding 1013. This phenomenon creates a conjugate problem: the Nusselt numbers depend on the radial temperature distribution of the disks, and the disk temperatures depend on the Nusselt numbers. Furthermore, Coriolis forces in the rotating fluid generate cyclonic and anticyclonic circulations inside the cavity. Such flows are three-dimensional, unsteady, and unstable, and it is a challenge to compute and measure the heat transfer from the disks to the axial throughflow in the compressor. In this paper, Nusselt numbers are experimentally determined from measurements of steady-state temperatures on the surfaces of both disks in a rotating cavity of the Bath compressor-cavity rig. The data are collected over a range of engine-representative parameters and are the first results from a new experimental facility specifically designed to investigate buoyancy-induced flow. The radial distributions of disk temperature were collected under carefully controlled thermal boundary conditions appropriate for analysis using a Bayesian model combined with the equations for a circular fin. The Owen-Tang buoyancy model has been used to compare predicted radial distributions of disk temperatures and Nusselt numbers with some of the experimentally determined values, taking account of radiation between the interior surfaces of the cavity. The experiments show that the average Nusselt numbers on the disk increase as the buoyancy forces increase. At high rotational speeds, the temperature rise in the core, created by compressibility effects in the air, attenuates the heat transfer, and there is a critical rotational Reynolds number for which the Nusselt number is a maximum. In the cavity, there is an inner region dominated by forced convection and an outer region dominated by buoyancy-induced flow. The inner region is a mixing region, in which entrained cold throughflow encounters hot flow from the Ekman layers on the disks. Consequently, the Nusselt numbers on the downstream disk in the inner region tend to be higher than those on the upstream disk.